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SAT Prep / Advanced Math / Function Notation
SAT Math · Advanced Math

Function NotationHow the SAT tests it — and how to beat it

Evaluating and composing functions written as f(x), interpreting what f(a) = b means, and translating between notation, tables, and graphs.

Practice Function Notation FreeAll of Advanced Math

Function Notation in Our Question Bank

30

Total questions

15

Easy

7

Medium

8

Hard

What the SAT Actually Tests

These questions strip functions down to the notation itself: given f(x) = 3x − 7, find f(4); given a table, find f(g(2)); or interpret a statement like f(20) = 12 in a real context. They're among the most learnable questions on the entire Math section.

Read f(input) = output every single time. For composition, work inside-out: evaluate the inner function first, then feed the result to the outer one. For interpretation questions, restate in words — f(20) = 12 means "when the input is 20 units, the output is 12 units" — then match to the choice that says exactly that.

Real Function Notation Practice Questions

Straight from the Grind1600 question bank — try each one before revealing the answer.

Question 1easy
The function g is defined by g(x) = x² - 3. Which of the following is equal to g(5)?
  • A)28
  • B)22
  • C)10
  • D)7
Show answer & explanation

Correct answer: B

Choice B is correct. Substituting 5 for x in the given function yields g(5) = 5² − 3 = 25 − 3 = 22.

Choice A is incorrect. This may result from adding 3 rather than subtracting it, giving 25 + 3 = 28.

Choice C is incorrect. This may result from interpreting x² as 2x, giving 2(5) = 10, and omitting the constant term.

Choice D is incorrect. This may result from interpreting x² as 2x, giving 2(5) − 3 = 7.

Question 2medium
If f(x) = x² - 3x and f(k) = 10, where k > 0, what is the value of k?
  • A)
  • B)
  • C)
  • D)
Show answer & explanation

Correct answer: 5

Set f(k) = 10: k² - 3k = 10. Rearranging: k² - 3k - 10 = 0. Factor: (k - 5)(k + 2) = 0. So k = 5 or k = -2. Since k > 0, k = 5.

Traps to Avoid

  • Evaluating f(g(x)) outside-in instead of inside-out.
  • Treating f(x + 2) as f(x) + 2 — a horizontal shift is not an output shift.
  • In context questions, swapping which real-world quantity is the input and which is the output.

More Advanced Math Skills

Equivalent Expressions

Rewriting algebraic expressions — factoring, expanding, combining rational expressions, and applying exponent rules to show two forms are equivalent.

Nonlinear Equations & Systems

Solving quadratic, radical, rational, and exponential equations, plus systems that mix a line with a curve — including discriminant reasoning.

Nonlinear Functions

Quadratic, exponential, and polynomial functions: vertex form, growth and decay, end behavior, and interpreting key features in context.

Master Function Notation With Adaptive Practice

30 Function Notation questions with step-by-step explanations, woven into a day-by-day study plan built for your test date.

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